Distance metric learning is a well studied problem in the field of machine learning, where it is typically used to improve the accuracy of instance based learning techniques. In this paper we propose a distance metric learning algorithm that is specialised for multi-label classification tasks, rather than the multiclass setting considered by most work in this area. The method trains an embedder that can transform instances into a feature space where squared Euclidean distance provides an estimate of the Jaccard distance between the corresponding label vectors. In addition to a linear Mahalanobis style metric, we also present a nonlinear extension that provides a substantial boost in performance. We show that this technique significantly improves upon current approaches for instance based multi-label classification, and also enables interesting data visualisations.